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Application of Abstract Differential Equations to Some Mechanical Problems (Paperback, Softcover reprint of the original 1st ed. 2003)
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Application of Abstract Differential Equations to Some Mechanical Problems (Paperback, Softcover reprint of the original 1st ed. 2003)
Series: Mathematics and Its Applications, 558
Expected to ship within 10 - 15 working days
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PREFACE The theory of differential-operator equations has been
described in various monographs, but the initial physical problem
which leads to these equations is often hidden. When the physical
problem is studied, the mathematical proofs are either not given or
are quickly explained. In this book, we give a systematic treatment
of the partial differential equations which arise in elastostatic
problems. In particular, we study problems which are obtained from
asymptotic expansion with two scales. Here the methods of operator
pencils and differential-operator equations are used. This book is
intended for scientists and graduate students in Functional Analy
sis, Differential Equations, Equations of Mathematical Physics, and
related topics. It would undoubtedly be very useful for mechanics
and theoretical physicists. We would like to thank Professors S.
Yakubov and S. Kamin for helpfull dis cussions of some parts of the
book. The work on the book was also partially supported by the
European Community Program RTN-HPRN-CT-2002-00274. xiii
INTRODUCTION In first two sections of the introduction, a classical
mathematical problem will be exposed: the Laplace problem. The
domain of definition will be, on the first time, an infinite strip
and on the second time, a sector. To solve this problem, a well
known separation of variables method will be used. In this way, the
structure of the solution can be explicitly found. For more details
about the separation of variables method exposed in this part, the
reader can refer to, for example, the book by D. Leguillon and E.
Sanchez-Palencia LS]."
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